Originally Posted by Xei
Theorem: Everybody on DreamViews loves Xei
Proof:
Proposition: any group of n people on DV have the same opinion of me.
Let's proceed by first assuming that the proposition is true for n  1; i.e., any group of n  1 people on DV have the same opinion of me.
Apply this to two groups, for example, person 1 through to person n  1, and person 2 through to person n.
It clearly follows that all of these people, person 1 through to person n, must have the same opinion of me.
In other words, if the proposition is true for n  1 people, it must be true for n people.
The proposition is clearly true for n = 1; any group of 1 person on DV has the same opinion of me as anybody else in the group, because a person must have the same opinion as themselves.
Hence, as the truth of n  1 implies the truth of n, as it is true for 1, it must be true for 2, and hence it must be true for 3, and hence...
and hence, it must be true for everybody in the forum.
Now that I have proved the proposition that everybody on DV has the same opinion of me, all that remains is to observe that at least one person, namely myself, loves me; and hence I have proved my theorem that everybody on DreamViews loves Xei.
Theorem: Everybody on DreamViews does not love Xei
Proof:
Proposition: any group of n people on DV have the same opinion of Xei.
Let's proceed by first assuming that the proposition is true for n  1; i.e., any group of n  1 people on DV have the same opinion of Xei.
Apply this to two groups, for example, person 1 through to person n  1, and person 2 through to person n.
It clearly follows that all of these people, person 1 through to person n, must have the same opinion of Xei.
In other words, if the proposition is true for n  1 people, it must be true for n people.
The proposition is clearly true for n = 1; any group of 1 person on DV has the same opinion of Xei as anybody else in the group, because a person must have the same opinion as themselves.
Hence, as the truth of n  1 implies the truth of n, as it is true for 1, it must be true for 2, and hence it must be true for 3, and hence...
and hence, it must be true for everybody in the forum.
Now that I have proved the proposition that everybody on DV has the same opinion of Xei, all that remains is to observe that at least one person, namely Aquanina, does not love Xei; and hence I have proved my theorem that everybody on DreamViews does not love Xei.


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